cheesemonkey wonders

cheesemonkey wonders

Sunday, January 19, 2020

Rooting Out Opportunity Hoarding and Perverse Incentives in the Math Classroom

tl;dr   The incentive structure of the math classroom is broken.

I live and teach in a community where opportunity hoarding is rampant. Students hoard points as if they were drops of water in the desert.

This leads to some perverse behaviors in the classroom. Students who have mastered a task or level want to take their attention to other parts of their lives. Their attitude is, I finished MY work; therefore MY obligations to math class are done. Students who have almost mastered a task or level of a topic become demanding of my attention in infantile ways. As soon as they run out of ideas, they tug on my sleeve, demanding that I re-teach them (or re-re-teach them) individually or in small groups. They value productive struggle only up to the point where they get stuck. The most challenged students feel so ashamed that they don't even know how to get started or even minimally unstuck that they try to hide in plain sight.

In a word, the incentive structure here is truly broken -- and perversely so.

I believe this is because the incentives here are all based on an assumption of individual attainment.

To allow a culture of individual attainment (what score /grade/mark did I get?) is to be complicit with the toxic culture of opportunity hoarding that pervades our whole society. I believe that the drive to hoard opportunity is one of the most powerful factors underlying the culture of systemic racism and oppression in schools.

Dylan Wiliam talks about how feedback needs to be more work for the recipient, yet every working classroom teacher I know knows that you can't force a kid to read or digest the comments. This is especially true when you have massive classes. With 37 kids per class, it's just not feasible. Kids look at the score and move on.

In my view, this is because the incentive structure of the math classroom is wrong. Not only is it wrong, it is sick and toxic. And we need to rethink these incentive structures if we truly want math class culture to heal.

If my grade means I personally have mastered or not mastered a topic, then once I get the score I want, my job is 100% done.

My problem with this is that, from the societal perspective, that is not my job as a classroom teacher.

My job as a classroom teacher is to get everybody over the finish line at the highest possible degree of mastery. For this reason,  my classroom's economy of achievement needs to become more collective, and less individual. I need to cultivate an incentive structure of positive interdependence -- "I" don't win unless others win too. Then we all win together.

There are times in my room when we're 37 individuals and there are other times when we are one classroom community. This is how things work on teams and in organizations throughout one's life in the U.S. So if we're one classroom community, then we need every individual to be as empowered as possible to achieve at the highest possible level.

For this reason, I've been expanding my whole-class skills quizzes. For a compound, complex skill such as solving a multi-step special right triangle problem (with interdependencies along the way), the quiz that I give is one that individuals take but each person's grade is an average of the scores of all the individuals in the class.

For two days leading up to the quiz, we do intensive collaborative work, including reciprocal doing-and-teaching practices such as speed dating. We also have unstructured time in which students identify as tutors or learners and then work to help each other improve the overall level of mastery in the room.

Our goal is a whole-class goal of mastery -- not an individual one. The goal is to raise the overall level of mastery in the room. Our goal as a class is to get everybody's level of understanding up. If you want to sit off to the side and work on your chemistry homework, then you're going to have to answer to your peers -- not to me. And if you don't like the grade that the whole class achieves, then too bad. Positive interdependence rules the day.

There are always one or two students who are so addicted to the toxic culture of individual attainment that they object, demanding, "If I understand it and they don't, then why should I be punished?"

And I have to explain to them over and over again. I tell them, "That's an infantile perspective. The better-prepared everyone around you is, the richer and more powerful your own learning experience is going to be -- both now and into the future. My job is to provide you with the richest possible learning experience so that you can go as far as you want to go. My job is to set the floor, not the ceiling. And this is how I, as the expert on learning, am empowering us to raise the floor of understanding."

Our school is unusual in that students get to choose their classes, their sections, and their teachers. My classes are very popular and are always among the earliest to fill up.

I choose to use this platform and my privilege to educate them. I'm blunt with the students who complain. "Listen," I tell them. "You chose this section. If you'd prefer a teacher who only gives individual scores on everything and lets you work on your chem homework when you're done, then we should talk to Counseling and get you into a course section where your desires are going to be met, because that's not going to happen in my class. There are plenty of other kids who'd be happy to switch with you."

I realize this may sound harsh, but they usually come around. And the fact is that my job is not to give them everything they think they want but to teach them and help them get aligned with the reality of things as they are.

The results bear this out. The lowest average on this first whole-class score of all my Geometry sections was an 87. The highest was 93.7.

The number of "free points" I provide in other parts of my class (through professionalism, home enjoyment packet completion, etc) makes this a wash. Nobody's grade goes down because of anybody else, but most people's grade do go up because their understanding improves. And as I tell them over and over and over again, what they need to do to raise their grades is to improve their understanding. The structure of the whole-class skills quiz empowers them to do so.

There's also less cheating and more cooperation because the incentive structures are aligned with our better, saner values.

There is still a place for individual attainment. Unit tests are individually graded as is the final exam. But individual attainment is demoted in my classroom and is put into better balance within our classroom community.

Individual attainment and opportunity hoarding are symptoms of our society's sickness. If we want to heal our learning environments and improve outcomes, we need to be open to revising the unconscious, unspoken incentive structures that keep reinforcing the systemic oppression we need to heal from.


@KarenCampe asks:
Wow this is amazing. Kudos to you for implementing something that really changes the game.
Do you have parent pushback?
— Karen Campe (@KarenCampe) January 19, 2020

I'm fortunate to have a lot of support from both site and district administration. In my view, this is a moral choice. My job is to create an equitable learning environment. If a parent were to insist on an inequitable learning environment for their child, I'm not sure what there is that we could do to satisfy them, given that this is public education.

Thanks for the question.

@timteachesmath asks:
Thank you for sharing! 
You've detailed your conversations with those 'done early'; 
what do those still learning think? Is there pressure to catch up, or a super supportive community?
— Tim (@timteachesmath) January 20, 2020

They appreciate that there is time and support being made for them to master what they find challenging. They want to learn the skills, but they get to do so in a way that does not punish them for needing more time or practice. They appreciate being part of the solution rather than part of the problem. And they are better able to participate and achieve their ends -- which is the goal. We are trying to normalize high achievement for everybody -- not sort out who "got it" first and who didn't.

Thanks for the question.

Saturday, January 4, 2020

How do we teach our students there are other ways to interact with the world beyond permanent war?

   My last encounter with physics did not leave me with a deep confidence in the practicality of math or science to save us. The course was taught by a man with no practical skills or insights or interpersonal skills, even though he was a tenured full professor at Princeton. What came through was that this was a man who allowed his wife to cut his hair using an upside-down bowl as a cutting guide. His hair was never even mildly symmetrical.

   I put my faith in medieval literary history instead.

   During the Dark Ages, clusters of monks in far-flung Irish monasteries kept the fires of learning lit. While the Vandal and Viking hoards stole, looted, burned, sacked, and traded away every last good thing the city-states and peoples of Western Europe had built, the Irish monks in remote scriptoria copied and illuminated manuscripts that preserved and spread the greatest learning of the day. And they taught their new generations how to carry out these vital matters of preservation and transmission along the way.

   When everyone else was taking cover and hoarding, the Irish monks kept learning alive, so that when the need – and demand – for it reawakened, it would be ready. Their system was like a beehive.  When it became possible again, the hives could be opened again and the contents could be used and shared for the public good.

   The desert is a lot like this. Things appear to have gone dead on the surface, but just below the veneer, the Earth is teeming with life – positively giddy with abundance.

   This is what gives me confidence to keep teaching and learning.

   It gives me confidence that something will survive until there is intelligent life in our world and in our government again.

    How do we keep the fires of learning lit in our society while those in power all around us seem to be losing their minds?

   We do it by putting our faith in our teaching.

   We do it by banding together – and by not letting go. We develop a hard, hard crust and we protect our water resources well. We do it by remembering that our job is to stay present with our students and teach them how math and science are opportunities to understand the divine. We remember that human beings at our best are thinking-based life forms. We remember to bond with our kids. We remember that the kids are always watching and that we have an opportunity to model the next right thing to do. We do it by remembering that teaching and learning are effervescent and holy.

Monday, December 16, 2019

Purpose and Meaning in a Final Exam

Ever since @CmonMattThink tweeted out this poster that I'm just nuts about, I've been thinking about all the different uses I have for this saying:

Today, as we're starting our final exam week, I'm thinking about it with regard to assessing the meaningfulness of a final exam. 

We give common departmental finals, which is why, when my normally independent 9th graders felt compelled to pepper me with questions about the majority of questions on the test, it made me notice and wonder about the test itself:

Is this test a scavenger hunt for right answers? Or does it measure students' ability to provide evidence of their understanding?

There was a previous conversation on Twitter a while back in which some of us were debating the allowability and rationale for allowing students to have a reference sheet on a test. Darryl Yong (@dyong, who you should follow if you're not already) said something that I 100% agree with: if I am measuring higher-order thinking and problem-solving, then THAT'S what I should be measuring and a reference sheet makes sense.

If I am measuring students' effectiveness at memorizing things (such as vocabulary terms), then a reference sheet doesn't make sense because memory and recall are what are being tested.

So right now I'm sitting in a ditch, frustrated by the fact that my Algebra 1 students have been run off the road because the current test is merely a scavenger hunt for right answers to memorized algorithms... when what I REALLY would like to be measuring and understanding is, Do my students know what to DO with their knowledge in both routine and non-routine situations?

And I hate this particular ditch.

Wednesday, October 2, 2019

Building a Feel for 'Major Moves' in Proof

This year I'm experimenting with developing students' intuition for and sense-making about what we call 'major moves' in proof.

Rather than ask students to buy into the illusion that two-column proofs emerge spontaneously and fully formed from their brow, we are inquiring into how we mortals can better brainstorm and use our reference tools to create the sub-assemblies that we can use to build our rough draft proofs. Then we'll be better able to polish our final proofs and present our work.

This has meant that we are developing students' intuition that that these sub-assemblies are knowable and predictable. We call these our "major proof moves." Some of our major categories of major proof moves include:

  • the relationships between parts & wholes
  • a sense of bisectors and "half-ness"
  • parallels and the results of parallels
  • perpendiculars and their results
  • right angles and their results.

It's working out surprisingly well.

Today we started experimenting with using these higher-order concepts to work on harder, multi-stage proofs. The kids were quite excited to be able to figure things out.

Every year I am amazed at how many times students have to repeat an experience before they get that "click." This is giving us a much wider field to wander in as we master the art of proof.

Friday, August 30, 2019

The First-Ever Block 5 Math Department Pot Luck Lunch

Today we had our first-ever block 5 Math Department pot luck lunch.

We have a very large department (24 teachers) and not all of us have the same block for lunch. The block 6 lunchers had a pot luck last week, and so fueled by the competitive spirit, the block 5 lunchers were mobilized by one of the least social people in the department to host our own pot luck. The sign-ups were on the corner one of the office white boards, so the menu was shaped over the last week. And since we have by far the largest crew, hopes were high that we could pull this off. And we did so -- with style.

I made the Lemongrass and Ginger Roast from the Field Roast cookbook because I've been wanting to try it and we have a surprisingly large number of vegans and people with significant food sensitivities. I rushed home from school yesterday so I could make it and set it on the stove to simmer. Sarah made a salad which I had been planning to use as a base for my new favorite school lunch (chef salad surprise). Ernie made an incredible, silky hummus and pita bread. Lisa made a shrimp and avocado ceviche. Raymond made a wonderfully spicy red lentil dal, which I still don't understand how he heated up but it was delicious. Tyler brought donuts. Scott baked a boule of crusty sourdough with cheese and sausage.

Not to scale
But the runaway winners of the day -- and in my opinion, the offerings that raised this pot luck to the level of Artistry -- were Robert's mother's fried chicken wings and Alex's made-to-order waffles.

Alex brought in his waffle iron and a killer cinnamon syrup that he had discovered on the internet. His TA worked the waffle-making station at the standing desk, making waffles to order and generally supervising (don't worry, we fed her).

That's right.

We. Had. Chicken. And. Waffles For. Lunch.

In. The. Math. Office.

And fresh-baked sourdough bread. And vegan charcuterie. AND DONUTS.
Who can turn down a good donut?

At one point, Art strolled in from the computer lab and felt bad that he hadn't brought anything. Everybody jumped in and chided him, "DON'T FEEL GUILTY -- WE ARE DROWNING IN FOOD." So he loaded up a plate and joined us.

I don't know why we never did this before.

As we were winding down, Lisa said, "I kind of have a math problem I wanted to ask about, but I don't want to spoil it."

And everybody jumped in again and said, "DON'T FEEL GUILTY." She sketched the problem and most of us started tinkering on scratch paper, but as usual, Robert saw straight through to the core of the simplification. We all put down our forks and pencils in shock at his surprising yet unsurprising clarity.

Then, of course, we needed another round of waffles.

It was the best community-building activity I've ever done. And it was basically free. I hope we do it again soon because Raymond's grandmother made these killer dim sum things for our end-of-school pot luck last year that nobody knows the name of but everybody devoured them. They look like little fried footballs with some kind of mystery meat or veggies inside their cavernous pockets. And they are TO DIE FOR.

Monday, July 29, 2019

Summer of Healing and Self-Care

I am sitting on the sofa in our dining room, deep in avoidance. I need to pack for the red-eye back east to see my family. There is thick silver cloud cover all the way down the hill to the bay and across the water. I can see a freighter which seems to be anchored on the water, but the East Bay hills, which I can usually see, are completely missing. Lost in the fog.

This has been my summer of self-care and healing. There have been too many deaths in my life this year. I needed time alone to grieve and to heal so I can turn the page and carry on. Fred always said, when it gets like this, it's time to turn inward. Focus on yourself. Ask, what is the best way I can use this situation for growth?

A big part of my work is focused on equity, but it has become a much more in-person thing and less online than ever before. I became the co-sponsor of our Black Student Union (BSU) and started raising money for them and advocating, mentoring, and learning alongside them. I started receiving awards this year for my equity work in my school and my community. On my end-of-year survey for the district's BSU program, the form asked, What is something you are most proud of this year? I wrote, "I raised over $8,000 for the programs and initiatives my Black students wanted to bring to fruition." The district BSU coordinator set up a phone appointment to follow up on our questionnaires. He asked me, "How did you DO that?" I told him, "I used my privilege and my connections, and I wouldn't take no for an answer."

I held my community accountable and I started to break through. And it made everybody feel much happier.

I won some actual awards for my work, but I don't like to focus on that. The actual ability to do this work is its own reward. I got some wonderful nods for an NPR commentary I did about what I am learning. And I realized I have found my path.

It was hard losing TMC because it got caught up in ripcurrents that were only partially about what they claimed to be about. That left an emptiness in my calendar in late July, but the harder thing was the loss of friendships I have cherished and come to rely on. I had to pack away gifts from former friends, wrapping them in tissue paper and tucking them into the back of a cabinet. It made me too sad to look at them. I received more hate-tweets and actual hate mail than I'd ever thought possible. I discovered Twitter's block function, but I learned it is only a mesh, not a wall. Hate still gets through.

I am learning how to develop a thicker skin.

I poured my energy into building our garden. Nothing heals like growing things. I spent days and weeks on end building and learning. It's become a sanctuary, a sacred space for growth. Now I'm studying hydroponics so I can grow lettuces and basil and tomatoes in the garden. Whole new parts of my mind and body are coming to life.

Now I'm headed east to visit family and to spend time down the shore, as we say in South Jersey. The garden is my West Coast bracket for healing. The warm waters of the Atlantic are my East Coast bookend. Connecting with family gives that healing burst of nutrients, and with my feet in the warm waters, I find nutrition for my next chapter of growth.

I think I will create a living wall in my classroom this year. A living wall and a Peace Corner. Some things are more important than math.

Friday, June 7, 2019

How I Started the Lowell Faculty Seminar on the Climate Emergency (and how you can too)

Towards the end of school, there's the narrowest of windows between the end of AP testing and the beginning of final exams when teachers at my school can sort of catch our breath. It's a week or two of relative down time for review and synthesizing and studying which reminds me of my beloved Reading Period at Princeton.

This year, I decided to put a stake in the ground and create an event so that our faculty community can make better use of this moment to collaborate in an interdisciplinary way on how we teach and learn about the climate crisis.

I have been reading and thinking about Project Drawdown's web site and NYT best selling book Drawdown, so I wrote a grant for a pilot project to get fifteen of our 200 faculty and staff together to help each other integrate climate change into our teaching.

The response was tremendous! So I wrote this blog post as a guide for myself and for anybody else who is like-minded about how I organized this faculty-led PD program -- and how you can do this with your faculty too.

In May, I ordered 15 copies of Drawdown and sent out this e-mail blast to the faculty inviting them to the Lowell Faculty Seminar on the Climate Emergency:
Hello colleagues -- 
   A new NPR/Ipsos poll shows that 86% of teachers say that students should learn about climate change... but only 42% teach it.  
   Because of this, it seems like the #1 thing we as a faculty can start doing about climate change is to talk about it -- and help each other understand it better.  
    So if you would like to read, learn, & discuss climate change with other Lowell teachers in a friendly, interdisciplinary way, then please join us (K__, C__, and E__, to start with) in the new Lowell Faculty Seminar on the Climate Emergency (aka the climate change book club).  
   SO, AFTER AP EXAMS -- To start things rolling, we will read and discuss Project Drawdown's NYT best selling book, Drawdown: The 100 most comprehensive plan ever proposed to reverse global warming: 
   This is a global problem so all are welcome! 
   Our short-term hope is to develop a common understanding, vocabulary, and framework for talking about climate change among the faculty. Our longer-term goal is to evolve some form of ongoing PD to help us integrate climate change across the curriculum. 
   GOOD NEWS! Thanks to A__'s and S__'s expert budget planning, we have 15 copies of Drawdown for teacher-participants who would like to join in this effort.
Please reply to this e-mail and let me know if you would like to join us (and if you would like to reserve a book).  
Elizabeth (Dr. S -- room 274) 
I received about 20 yeses, of which 15 turned out to be viable. During my prep blocks, I went around distributing books and introducing myself to staff across the faculty and across the campus who were interested. It was great to meet colleagues in English, Social Studies, Ethnic Studies, Peer Resources, World Languages, Academic Counseling, and Physical Education who were thinking about the climate crisis too, in addition to us nerds in math and science.

We used a Doodle poll to find an available after-school hour and I sent out a message confirming time and place and logistics. Everyone committed to reading the three introductory sections of Drawdown in preparation for our kickoff meeting.

The first meeting focused on introductions, intentions, and the basic science of the climate crisis. Our goal was/is to map out topics, strategies, and projects on which we could collaborate over the next year in our work together. Many other teachers who were not available for our kickoff meeting also expressed interest in these conversations over the next year.

In an interdisciplinary context, it felt essential to make sure that everybody -- including colleagues in non-quantitative fields -- felt equally empowered by the science rather than intimidated. I served as the seminar leader and ran the agenda, even though it was intimidating to do so in front of our two National Board Certified AP Environmental Sciences teachers and a number of other accomplished science teachers.

One benefit of my being the one to lead the meeting -- as a math teacher, meditator, writer, Black Student Union advisor, and member of the school's equity leadership team -- was that I could bring slightly different lenses to the process of discussing the climate.


I asked for the group's indulgence to begin with a slightly different opening ritual than we usually use at our PWAI (Predominantly White and Asian Institution)  -- a LAND ACKNOWLEDGMENT.  We stood and I read this draft of our statement:
Before we begin...
We pause to acknowledge that Lowell sits on the traditional lands of the Ohlone people, who are the indigenous stewards of this beautiful place we teach and learn on. We acknowledge their ancient and federally unrecognized claim on this land, their enslavement in our city, and our own uncomfortable role in this history. We do this to pay respect to all Ohlone people, past, present, and future.
This led to an amazing and heartfelt discussion. We talked about the fact that we have Native Americans in all parts of our school -- on the faculty, in our staff, in our alumni community, and in our student body -- and that this is something we need to acknowledge in order for everybody to feel seen and included.

The faculty of color at our meeting expressed surprise that they had not previously experienced this kind of ritual at an official school event, and everyone expressed interest in having us integrate these acknowledgments into our future events as well.

For many of us, it has been years since we've formally studied the science of climate change, so it seemed important to set our initial level of understanding. I used this video by noted climate scientist and explainer, Katharine Hayhoe, of Texas Tech University to kick off our discussion of the science:

We followed this up with an open discussion as well as questions from the non-science teachers. The "1.5 to 2 degrees" limit proved to be a very fruitful hook which everybody was eager to use in their pedagogical thinking.

A big part of introducing the climate crisis into our pedagogy involves using current and appropriate language for framing our discussions. This brief opinion piece by the Environment Editor of The Guardian newspaper gave our English teacher member an on-ramp to lead the next part of our discussion:
What role do our language choices -- both conscious and unconscious -- play in how we teach and learn about the climate crisis? Is it sufficient to call it "climate change" or is it more accurate to use terms like "climate emergency"?

T__ was particularly interested in using this op-ed with her Critical Writing classes, although everybody wanted to do more thinking about the effects of the language we use, so we stuck a pin in this as a topic we would like to collaborate on over the next year of our meetings.

Even though we teach and learn together in liberal San Francisco, which is an admittedly friendly context for mobilizing about science, we all admitted frustration over the frequency with which we encouter climate science denialism.

I introduced the free, self-paced MOOC (massive open online course) I have started taking from edX, offered by the University of Queensland in Australia, called Making Sense of Climate Science Denial:
In particular, their chart on the five characteristics of science denial found immediate fans and a home in our soon-to-be-revised Critical Writing course:
FLICC acronym (Fake experts, Logical fallacies, Impossible expectations, Cherry picking, Conspiracy theories)
Several colleagues promptly expressed their intention to take this course over the summer.

The New York Times provided a timely article from the previous day about how the Trump administration is doubling down on its attacks on climate science:
 This prompted a discussion about how we can integrate current news stories into our curriculum.

We set our intention to meet monthly during the next school year and also to set up an e-mail alias for ease of communications.

Over the next two weeks, I heard from so many participants and soon-to-be participants about how valuable they felt this was. It really drove home the message of Katharine Hayhoe's viral TED talk: that the most important thing we citizens -- and particularly teachers -- can do about the climate emergency is to start talking about it.